Finite Group Databasebeta

← #25159630

Subgroups — #25159630

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583183C211yesmaximal, characteristic, complemented
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138446C211yesmaximal, characteristic
4#19137509C211yesmaximal, characteristic, complemented
5#19136125C211yesmaximal, characteristic
6#19136075C211yesmaximal, characteristic, complemented
7#19135964C211yesmaximal, characteristic
8#19135927C211yesmaximal, characteristic, complemented
9#19135152C211yesmaximal, characteristic, complemented
10#19134951C211yesmaximal, characteristic
11#19134951C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134860C211yesmaximal, characteristic, complemented
14#19134855C211yesmaximal, characteristic
15C43×#1941C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063303—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583183—24no—
24C4×#10621873—24no—
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35#14582823—21no—
36#14582812—21no—
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582796—21no—
41#14582795C2211yescharacteristic
42#14582794—21no—
43#14582770—21no—
44#14582768—21no—
45#14582768C2211yescharacteristic
46C4×Dic43⋊C4C2211yescharacteristic
47#14582750—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873Q814yescomplemented
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324—41no—
72#13063303—44no—
73C4×Dic86—22no—
74C4×Dic86—41no—
75#13063290—22no—
76#13063290—22no—
77#13063290—22no—
78#13063290—41no—
79C4×D172—22no—
80C4×D172—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4D411yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103#13063257—22no—
104#13063256—22no—
105#13063256—41no—
106Dic43⋊C8—22no—
107#13063250D414yes—
108#13063248—22no—
109#13063248—22no—
110#13063247—22no—
111#13063245—22no—
112#13063245—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126#106×C43—22no—
127#106×C43—22no—
128C4×C8×C43—22no—
129#95×C43—21no—
130#95×C43—21no—
131C23×D43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C2×Q812yes—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—81no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—42no—
159C2×Dic86—42no—
160C2×Dic86—81no—
161C2×Dic86C2×D412yes—
162C2×Dic86C2×Q812yes—
163C2×Dic86#4112yes—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D412yes—
169C2×C8×C43C2×Q812yes—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43#4112yes—
180C42×C43—21no—
181C42×C43—21no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—81no—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—41no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200Dic43⋊C4SD1614yescomplemented
201C4×Dic43—24no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—42no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214#10621873—28no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C2×SD1612yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43C2×SD1612yes—
267C2×Dic43C2×SD1612yes—
268D172—22no—
269D172—22no—
270D172—41no—
271D172—41no—
272C4×D43—84no—
273Dic86—22no—
274Dic86—22no—
275Dic86—22no—
276Dic86—84no—
277Dic86C22⋊Q814yescomplemented
278C8×C43—22no—
279C8×C43—22no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#26373—431nomaximal, Sylow
283C22×C43#52511yescharacteristic
284C22×C43D4211yescharacteristic
285C22×C43D4×Q811yescharacteristic
286C22×C43C22×SD1611yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57711yescharacteristic
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C4×C43—22no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43C2×C22⋊Q811yescharacteristic
304C4×C43#53911yescharacteristic
305C4×C43#54711yescharacteristic
306C4×C43#55411yescharacteristic
307Dic43—22no—
308Dic43—24no—
309Dic43—22no—
310Dic43—41no—
311Dic43—41no—
312Dic43—42no—
313Dic43—81no—
314C2×#475—431no—
315C2×C4×SD16—431no—
316#2452—431no—
317Q8×C4⋊C4—431no—
318#2094—431no—
319#2084—431no—
320#2065—431no—
321#2058—431no—
322#1941D4311yescharacteristic, complemented
323#1916—431no—
324#1880—431no—
325#1880—431no—
326#1865—431no—
327#1865—431no—
328#1864—431no—
329C2×C43#244911yescharacteristic
330C2×C43#310311yescharacteristic
331C2×C43#312511yescharacteristic
332C2×C43#327111yescharacteristic
333C2×C43D4×SD1611yescharacteristic
334C2×C43Q8×SD1611yescharacteristic
335C2×C43#338811yescharacteristic
336D43—82no—
337C22×SD16—431no—
338C2×C4⋊Q8—431no—
339C2×C22⋊Q8—861no—
340C2×C4×Q8—431no—
341C2×C4×Q8—431no—
342C2×C4×Q8—431no—
343C2×C4×D4—431no—
344#475—864no—
345C4×SD16—864no—
346C2×#106—431no—
347C2×#106—431no—
348C2×#106—431no—
349C2×#106C2×D4311yescharacteristic
350C2×#106C2×D4311yescharacteristic
351C2×C4⋊C8—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×C4×C8C2×D4311yescharacteristic
359#396—861no—
360#393—861no—
361#390—431no—
362#390—431no—
363#389—431no—
364#389—431no—
365#389—861no—
366#389—861no—
367#389C2×D4311yescharacteristic
368#389C2×D4311yescharacteristic
369#385—861no—
370#384—431no—
371#384—861no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—861no—
374#340—431no—
375#340—431no—
376#340C2×D4311yescharacteristic
377#340C2×D4311yescharacteristic
378#336—431no—
379#336—431no—
380#336—431no—
381#336—431no—
382C43#2637311yescharacteristic, complemented, Sylow
383C22×Q8—431no—
384C22×Q8—861no—
385C22×D4—431no—
386C23×C4—861no—
387C2×SD16—434no—
388C2×SD16—862no—
389C2×SD16—862no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394C4⋊Q8—862no—
395C4⋊Q8—1721no—
396C22⋊Q8—1724no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—1721no—
402C4×Q8—1721no—
403C4×D4—862no—
404C4×D4—1721no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#106—22no—
435#106—22no—
436#106—862no—
437#106—862no—
438#106—1721no—
439C4⋊C8—862no—
440#103—434no—
441#103—862no—
442#103—862no—
443#102—862no—
444#102—862no—
445#102—1721no—
446C4×C8—22no—
447#95—21no—
448#95—21no—
449#95—431no—
450#95—431no—
451#95—861no—
452#95—861no—
453C24—861no—
454C2×Q8—432no—
455C2×Q8—432no—
456C2×Q8—432no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—3441no—
461C2×Q8—1722no—
462C2×Q8—1722no—
463C2×D4—432no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—3441no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486SD16—868no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8D4×D4312yes—
498C2×C8Q8×D4312yes—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—81no—
508C4⋊C4—434no—
509C4⋊C4—432no—
510C4⋊C4—864no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—3441no—
515C4⋊C4—3441no—
516C4⋊C4—1721no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4#1062189812yes—
523C22⋊C4—3441no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C42—21no—
529C42—21no—
530C42—864no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—1722no—
536C42—1722no—
537C23—862no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23C2×D4×D4311yescharacteristic
545Q8—434no—
546Q8—862no—
547Q8—862no—
548Q8—862no—
549Q8—3444no—
550D4—862no—
551D4—862no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—862no—
574C2×C4—861no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—862no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—862no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4SD16×D4312yes—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4C2×#1062189811yescharacteristic
598C2×C4#1306337111yescharacteristic
599C2×C4#1306337311yescharacteristic
600C8—22no—
601C8—22no—
602C8—1721no—
603C8—1721no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—1722no—
609C22—1722no—
610C22—1722no—
611C22#1458340811yescharacteristic
612C22#1458353311yescharacteristic
613C22#1458356411yescharacteristic
614C22C2×SD16×D4311yescharacteristic
615C22#1458369611yescharacteristic
616C22#1458370511yescharacteristic
617C22#1458370611yescharacteristic
618C4—22no—
619C4—42no—
620C4—41no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—862no—
625C4—864no—
626C4—862no—
627C4—3441no—
628C4—1722no—
629C4—1721no—
630C4—1721no—
631C4C22⋊Q8×D4311yescharacteristic
632C4#1458349711yescharacteristic
633C4#1458355011yescharacteristic
634C4#1458360911yescharacteristic
635C2—3442no—
636C2#1913841111yescharacteristic
637C2#1914462411yescharacteristic
638C2#1914486811yescharacteristic
639C2#1914617711yescharacteristic
640C2#1914628811yescharacteristic
641C2#1914745211yescharacteristic
642C2#1914754611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1941C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1941D43
hypocenterC43#26373
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583183C2semidirect
4. #19137509C2semidirect
6. #19136075C2semidirect
8. #19135927C2semidirect
9. #19135152C2semidirect
12. #19134862C2semidirect
13. #19134860C2semidirect
15. C43×#1941C2semidirect
67. C2×#10621873Q8semidirect
200. Dic43⋊C4SD16semidirect
277. Dic86C22⋊Q8semidirect
322. #1941D43semidirect
382. C43#26373semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145831832
C2×C4×#106218732
#191384462
#191375092
#191361252
#191360752
#191359642
#191359272
#191351522
#191349512
#191348622
#191348602
#191348552
C43×#19412
#2637343